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Mandelbrot Set in Excel using MakeArray

This post shares how to create a simple Mandelbrot set in Excel using the function MAKEARRAY.

We ease into things by starting with a simple shape: a square. And with the basics established we can tackle making the more complex Mandelbrot set.

Technically, everything we make will be a rectangle, but the shape emerges from the content of the cells. Just as an artist paints to the edge of a canvas, the function MAKEARRAY generates an N x M matrix. It will set the content of each cell to the result of a lambda function and with conditional formatting to color the area a shape emerges.

The following demonstrates creating a matrix and filling it with the values provided to the lambda function.

5 x 5 Matrix

To create a square we can populate the edges with ‘#’ and leave the center blank. The simplest way to do this is…

Simple Square

The approach above works but has a fixed size. This can be improved upon to allow the size to be provided…

We can also accept optional input for the edge character…

And while we’re at it, we can fill the square with another character…

Adding conditional formatting gives it “pizzazz”.

Conditional Formatting

It consists of two functions…

MANDELBROT

The above should be added as named ranges. It can be called with a size, e.g. 200.

The output can be conditionally formatted with a color scale.

Conditional format with Color Scales

The initial result…

The result can be improved by using a 3-Color Scale…

3-Color Scale with midpoint of 70

The power of lambda functions continues to impress me. Let me know if you find a set of values for the 3-Color scale that gives a more striking result.

An improvement to this would be to accept inputs for the cx, cy variables.

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